Wireless Communication Apparatus

ABSTRACT

This invention relates to methods, apparatus, and processor control code for signal detection in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexed (MIMO-OFDM) communications systems. A method for determining outputs from a received signal in a lattice-reduction-aided receiver based multi-carrier wireless communications system having a plurality of sub-carriers divided into a plurality of sets of sub-carriers, the method comprising performing a detection method for each of said sets, the detection method comprising the step of applying lattice reduction to said set of sub-carriers thereby generating a reduced basis channel response.

CROSS-REFERENCE OF APPLICATION

This application is based on and claims priority to United KingdomPatent Application 0610847.6, filed Jun. 1, 2006, the entire contents ofwhich is incorporated herein.

FIELD OF INVENTION

This invention relates to methods, apparatus, and processor control codefor signal detection in Multiple Input Multiple Output (MIMO)communications systems. More particularly, it relates to signaldetection in MIMO Orthogonal Frequency Division Multiplexed (MIMO-OFDM)communications systems.

BACKGROUND OF THE INVENTION

Conventional communication systems can be represented mathematically as:y=Hx+vin which, for a MIMO communication system, y is an n-by-1 vectorrepresenting the received signal, H is an n-by-m channel matrixmodelling the transmission characteristics of the communicationschannel, x is an m-by-1 vector representing transmit symbols, v is ann-by-1 noise vector and wherein m and n denote the number of transmitand receive antennas respectively.

Recent publications have demonstrated how the use of a technique calledLattice Reduction can improve the performance of MIMO detection methods.

For example, “Lattice-Reduction-Aided Detectors for MIMO CommunicationSystems”, (H. Yao and G. W. Wornell, Proc. IEEE Globecom, November 2002,pp. 424-428) describes Lattice-reduction (LR) techniques for enhancingthe performance of multiple-input multiple-output (MIMO) digitalcommunication systems.

In addition, “MMSE-Based Lattice-Reduction for Near-ML Detection of MIMOSystems”, (D. Wubben, R. Bohnke, V. Kuhn and K. Kammeyer, in Proc. ITGWorkshop on Smart Antennas, July 2004, pp. 106-113, hereinafter referredto as “Wubben et al.”) adopts the lattice-reduction aided schemes to theMMSE criterion.

“From lattice-reduction-aided detection towards maximum-likelihooddetection in MIMO systems”, (C. Windpassinger, L. H.-J. Lampe and R. F.H. Fischer, in Wireless and Optical Communications, WOC 2003) extendsthe lattice-reduction-aided detection scheme described in Wubben et al.with the use of the well-known LLL algorithm, which enables theapplication to MIMO systems with arbitrary numbers of dimensions.

Furthermore, “Lattice reduction aided pre-coding”, (C. Windpassinger, R.F. H. Fischer and J. B. Huber, in IEEE Transactions on Communications,December 2004, vol. 52, issue 12. pp. 2057-2060) shows the use oflattice reduction applied to MIMO pre-coding.

The techniques used in the publications described above use the conceptthat mathematically, the columns of the channel matrix, H, can be viewedas describing the basis of a lattice. An equivalent description of thislattice (a so-called ‘reduced basis’) can therefore be calculated sothat the basis vectors are close to orthogonal. The MIMO receiver, orpre-coder, can employ this reduced basis to equalize the channel,yielding a significant performance advantage over a non-lattice aidedlinear detector or pre-coder.

Orthogonal Frequency Division Multiplexing (OFDM) is a well-knowntechnique for transmitting high bit rate digital data signals. Ratherthan modulate a single carrier with the high speed data, the data isdivided into a number of lower data rate channels each of which istransmitted on a separate subcarrier. MIMO-OFDM based systems are likelyto form the core of future wireless communication standards, for examplethe IEEE 802.11n WLAN standard.

For example, “Lattice-Reduction-Aided Receivers for MIMO-OFDM in SpatialMultiplexing Systems” (I. Berenguer, J. Adeane, I. Wassell and X. Wang,in Proc. Int. Symp. on Personal Indoor and Mobile Radio Communications,September 2004, pp. 1517-1521, hereinafter referred to as “Berenguer etal.”) describes that Lattice-reduction techniques can be applied toMIMO-OFDM based systems and can yield a significant performanceadvantage over other reduced complexity detection techniques (such as,as illustrated in FIGS. 6 to 9 in Berenguer et al.).

“Improved detection methods for MIMO-OFDM-CDM communication systems” (J.Adeane, M. R. D. Rodrigues, I. Berenguer, and I. J. Wassell, in Proc.IEEE Vehicular Technology Conference (VTC 2004), September 2004, pp.1604-1608, hereinafter referred to as “Adeane et al.”) applies MIMOdetection methods based on lattice reduction, partial decision feedback(PDF), and BLAST ordering techniques to MIMO-OFDM-CDM systems.

Berenguer et al. and Adeane et al. employ the most common latticereduction algorithm, the Lenstra-Lenstra-Lovasz (LLL) algorithmdisclosed in “Factoring Polynomials with Rational Coefficients”, (A.Lenstra, H. Lenstra and L. Lovasz, Math Ann., Vol. 261, pp. 515-534,1982, hereinafter referred to as “Lenstra et al.”), on a per-sub-carrierbasis. However, none of the above literature discusses the principle ofapplying the LLL algorithm, or any other lattice reduction algorithm, togroups of sub-carriers.

A MIMO detector which employs lattice reduction on a per-sub-carrierbasis 200 is shown in FIG. 3. In Step S1-2 in FIG. 3, the channelmatrix, H_(k), for sub-carrier k, is obtained.

According to Step S1-4, the channel matrix, H_(k), for sub-carrier k, isdecomposed into:H_(k)=Q_(k)R_(k)using a standard QR decomposition, or any of its sorted variants. TheLLL algorithm, or more generally, any suitable lattice reductionalgorithm S1-6, can then be applied to Q_(k) and R_(k):[T_(k), Q _(k), R _(k)]=LLL(Q_(k),R_(k),P)where, P is a permutation matrix S1-8, which in this configuration isnormally initialised to be an identity matrix with the same dimensionsas H. The LLL algorithm produces:H_(k)T_(k)={tilde over (Q)}_(k){tilde over (R)}_(k)which describes the reduced lattice for sub-carrier k. This process isrepeated for all N sub-carriers independently S1-10. As shown in FIG. 3,this per-sub-carrier lattice reduction process, which requires a QRdecomposition S1-4 and lattice reduction S1-6 per sub-carrier.

It should be noted that the LLL algorithm in its standard form employsan iterative technique, where it is not known a-priori how manyiterations it will take before the algorithm converges. This means thatthe complexity of the algorithm is variable and dependant upon thematrix to be reduced.

The lattice reduction detectors for MIMO-OFDM systems described in theabove references all assume that the LLL algorithm (although any otherlattice Reduction algorithm could be employed) is applied on aper-sub-carrier basis. This per-sub-carrier lattice reduction representsa significant proportion of the overall detector complexity. Therefore,it is desirable to reduce the complexity of this stage of the detectoralgorithm.

For example, in Berenguer et al., a MIMO-OFDM system with 16information-bearing sub-carriers is considered. In that method, the LLLalgorithm is applied independently to the channel matrix for eachindividual sub-carrier, as described above. This process must beundertaken for each OFDM packet received. In future MIMO-OFDM WLANsystems, such as IEEE 802.11n, it is expected that 52 or moreinformation bearing sub-carriers will be employed. In future cellularsystems, where this technique is equally applicable, there may behundreds of active sub-carriers, each of which requires latticereduction.

SUMMARY OF THE INVENTION

There is therefore a need to reduce the complexity of the basisreduction of each sub-carrier channel matrix for a multi-carrier system.

Embodiments of the invention include apparatus and methods fordetermining outputs from a received signal in a lattice-reduction-aidedreceiver based multi-carrier wireless communications system.

In a first aspect of the present invention there is provided a methodfor determining outputs from a received signal in alattice-reduction-aided receiver based multi-carrier wirelesscommunications system having a plurality of sub-carriers divided into aplurality of sets of sub-carriers, the method comprising performing adetection method for each of said sets, the detection method comprisingthe step of applying lattice reduction to said set of sub-carriersthereby generating a reduced basis channel response.

In an embodiment of the present invention, said method further comprisesthe step of determining a single value channel response matrix from aset of channel response matrices.

The step of determining said single value channel response may beperformed by any one of:

-   -   i. mean value of said channel response matrices, and;    -   ii. median value of said channel response matrices.        In another embodiment of the present invention, said method        further comprises the step of processing said single value        channel response matrix thereby generating an unitary matrix and        a triangular matrix.

The step of processing said single value channel response matrix may bea QR decomposition of said single value channel response matrix.

Preferably, the step of applying said lattice reduction to saidplurality of sub-carriers includes the step of applying said latticereduction to said unitary matrix and said triangular matrix.

In another embodiment of the present invention said method furthercomprises the step of determining a reduced basis of a sub-carrier inaccordance with said reduced basis channel response.

In another embodiment of the present invention, the method furthercomprises the step of determining a unitary matrix and a triangularmatrix for said sub-carrier.

The step of determining an unitary matrix and a triangular matrix forsaid sub-carrier may be performed by any one of:

-   -   i. A QR decomposition, and;    -   ii. An interpolation method.

Preferably, the lattice reduction is in accordance with the LLLalgorithm.

Preferably, the LLL algorithm provides the following relationship:[ T,{tilde over (Q)}_(k),{tilde over (R)}_(k)]=LLL( Q _(k), R _(k),P)

-   -   where P is a permutation matrix.

Preferably, said permutation matrix comprises an identity matrix.

In another embodiment of the present invention, said method furthercomprises the step of applying lattice reduction to said unitary matrixand the relationship of said triangular matrix to said sub-carrier is:[T_(k),{tilde over (Q)}_(k),{tilde over (R)}_(k)]=LLL({tilde over(Q)}_(k),{tilde over (R)}_(k),{tilde over (T)})

-   -   where T is a permutation matrix.

In a further aspect the invention provides an apparatus for determiningoutputs from a received signal in a lattice-reduction-aided receiverbased multi-carrier wireless communications system having a plurality ofsub-carriers divided into a plurality of sets of sub-carriers, theapparatus comprising detection means for performing detection on each ofsaid sets, the detection means comprising means for applying latticereduction to said sub-carriers in said set thereby generating a reducedbasis channel response.

The invention further provides a receiver incorporating an apparatus asdescribed above.

The skilled person will recognise that the above-described apparatus andmethods may be implemented using and/or embodied in processor controlcode. Thus in a further aspect the invention provides such code, forexample on a carrier medium such as a disk, CD- or DVD-ROM, programmedmemory such as read-only memory (Firmware) or on a data carrier such asan optical or electrical signal carrier. Embodiments of the inventionmay be implemented on a DSP (Digital Signal Processor), ASIC(Application Specific Integrated Circuit) or FPGA (Field ProgrammableGate Array). Thus the code may comprise conventional program code, ormicro-code, or, for example, code for setting up or controlling an ASICor FPGA. In some embodiments the code may comprise code for a hardwaredescription language such as Verilog (Trade Mark), VHDL (Very high speedintegrated circuit Hardware Description Language), or SystemC. As theskilled person will appreciate, processor control code for embodimentsof the invention may be distributed between a plurality of coupledcomponents in communication with one another.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates schematically a MIMO system including a transmitterand a receiver;

FIG. 2 illustrates in further detail the receiver of FIG. 1;

FIG. 3 illustrates a conventional per-sub-carrier lattice reductionprocess;

FIG. 4 illustrates a cooperative basis reduction process formulti-carrier communications systems in accordance with a firstembodiment of the present invention;

FIG. 5 illustrates a group basis reduction process for multi-carriercommunications systems in accordance with a second embodiment of thepresent invention;

FIG. 6 illustrates the performance of the basis sub-carrier groupingmethod in comparison with the per-sub-carrier method in accordance withan embodiment of the present invention.

DETAILED DESCRIPTION

The present invention will be described in further detail on the basisof the attached diagram.

FIG. 1 illustrates such a system, comprising a MIMO data communicationssystem 10 of generally known construction. New components, in accordancewith a specific embodiment of the invention, will be evident from thefollowing description.

The communications system 10 comprises a transmitter device 12 and areceiver device 14. It will be appreciated that, in many circumstances,a wireless communications device will be provided with the facilities ofa transmitter and a receiver in combination but, for this example, thedevices have been illustrated as one way communications devices forreasons of simplicity.

The transmitter device 12 comprises a data source 16, which providesdata (comprising information bits) to a baseband mapping unit 20, whichoptionally provides forward error correction coding, channelinterleaving and which outputs modulated symbols. The modulated symbolsare provided to a multiplexer 22 which combines them with pilot symbolsfrom a pilot symbol generator 18, which provides reference amplitudesand phases for frequency synchronisation and coherent detection in thereceiver and known (pilot and preamble) data for channel estimation. Themultiplexed symbols are provided to a parser 24, which creates aplurality of parallel spatial streams. The combination of blocks 26, 28and 30 convert the serial spatial data stream from parser 24 to aplurality of parallel, reduced data rate streams, performs an IFFT onthese data streams to provide an OFDM symbol, and then converts themultiple subcarriers of this OFDM symbol to a single serial data stream.Processes 26, 28 and 30 are performed in parallel for each spatialstream. The space-time encoder 32 encodes an incoming symbol or symbolsas a plurality of code symbols for simultaneous transmission from atransmitter antenna array 34 comprising a plurality of transmitantennas. In this illustrated example, two transmit antennas areprovided, though practical implementations may include more antennasdepending on the application.

The encoded transmitted signals propagate through a MIMO channel 36defined between the transmit antenna array 34 and a correspondingreceive antenna array 38 of the receiver device 14. The receive antennaarray 38 comprises a plurality of receive antennas which provide aplurality of inputs to a parallel bank of blocks 40, 42 and 44 whichperform a serial-to-parallel conversion, FFT, and parallel-to-serialre-conversion independently for each received stream, providing anoutput to the lattice-reduction-aided decoder 46. In this specificembodiment, the receive antenna array 38 comprises two receive antennas.

The lattice-reduction-aided decoder 46 has the task of removing theeffect of the MIMO channel 36. The output of the lattice-reduction-aideddecoder 46 comprises a plurality of signal streams, one for eachtransmit antenna, each carrying so-called soft or likelihood data on theprobability of a transmitted bit having a particular value. This data isprovided to a de-parser 48 which reverses the effect of the parser 24,and the de-parsed bits output by this de-parser 48 are then presented toa de-multiplexer 50 which separates the pilot symbol signal 54 from thedata symbols. The data symbols are then demodulated and de-mapped bybase-band de-mapping unit 52 to provide a detected data output 56.Broadly speaking the receiver 14 is a mirror image of the transmitter12. The transmitter and receiver may be combined to form an OFDMtransceiver.

The specific function of the lattice-reduction-aided decoder 46 will bedescribed in due course.

FIG. 2 illustrates schematically hardware operably configured (by meansof software or application specific hardware components) as the receiverdevice 14. The receiver device 14 comprises a processor 110 operable toexecute machine code instructions stored in a working memory 112 and/orretrievable from a mass storage device 116. By means of a generalpurpose bus 114, user operable input devices 118 are capable ofcommunication with the processor 110. The user operable input devices118 comprise, in this example, a keyboard and a mouse though it will beappreciated that any other input devices could also or alternatively beprovided, such as another type of pointing device, a writing tablet,speech recognition means, or any other means by which a user inputaction can be interpreted and converted into data signals.

An alternative implementation could also include a transceiver withoutpredefined user interface.

Audio/video output hardware devices 120 are further connected to thegeneral purpose bus 114, for the output of information to a user.Audio/video output hardware devices 120 can include a visual displayunit, a speaker or any other device capable of presenting information toa user.

Communications hardware devices 122, connected to the general purposebus 114, are connected to the receive antennas 26. In the illustratedembodiment in FIG. 2, the working memory 112 stores user applications130 which, when executed by the processor 110, cause the establishmentof a user interface to enable communication of data to and from a user.The applications in this embodiment establish general purpose orspecific computer implemented utilities that might habitually be used bya user.

Communications facilities 132 in accordance with the specific embodimentare also stored in the working memory 112, for establishing acommunications protocol to enable data generated in the execution of oneof the applications 130 to be processed and then passed to thecommunications hardware devices 122 for transmission and communicationwith another communications device. It will be understood that thesoftware defining the applications 130 and the communications facilities132 may be partly stored in the working memory 112 and the mass storagedevice 116, for convenience. A memory manager could optionally beprovided to enable this to be managed effectively, to take account ofthe possible different speeds of access to data stored in the workingmemory 112 and the mass storage device 116.

On execution by the processor 110 of processor executable instructionscorresponding with the communications facilities 132, the processor 110is operable to establish communication with another device in accordancewith a recognised communications protocol.

In the present embodiment, prior to the processing stage, it is assumedthat the sub-carriers have been grouped into sets. These sets need notbe of uniform size. The size of the sets will be a function of thefrequency selectivity of the channel, i.e. in the case where the channelhas low frequency selectivity, adjacent sub-carriers are highlycorrelated and therefore large sets may be employed. At the otherextreme, where a highly frequency selective channel is encountered, thesets may contain only a small number of sub-carriers. The allocation ofsub-carriers to sets may be accomplished dynamically depending upon thechannel conditions, or it may be fixed.

The manner in which this grouping is achieved is immaterial: anyappropriate sub-carrier grouping technique may have been used.

In the following description, without loss of generality, K sub-carriersare allocated to each set. Basis reduction is described for a single setwith the method being repeated identically for the remaining sets.

Referring to FIG. 4, the following 5 stages are performed on a per-setbasis:

1. Firstly, in step S2-2, the process is initialised for a set derivedfrom the channel matrix. As noted in step S2-4 in FIG. 4, and referredto as “CSI processing” a single value, H, is computed to be input to thelattice reduction algorithm from the set of H_(k). It is possible toemploy a number of different metrics to achieve this. In this embodimentthe mean value is derived as follows:$\overset{\_}{H} = {\frac{1}{K}{\sum\limits_{k = 0}^{K - 1}\quad H_{k}}}$Other metrics, such as the modal or median value, or one of theindividual H_(k) could be employed as the basis of H.

2. As identified in step S2-6, QR, or sorted QR, decomposition isapplied to the matrix H to yield Q and R.

3. Basis reduction is applied using the LLL algorithm S2-8 applied to Qand R. This step also calls upon initialisation, in step S2-10, of apermutation matrix P such that it is a suitably dimensioned identitymatrix in this method. The LLL function will yield T, {tilde over (Q)}and {tilde over (R)} for the average channel transfer function, so thatHT={tilde over (QR)}.

It will be appreciated that any other suitable basis reduction algorithmcould be used instead.

4. The reduced basis for each sub-carrier H_(k) T is computed in stepS2-12.

5. Finally, in step S2-14, the reduced basis for each sub-carrier (QR,or sorted QR) is decomposed to yield Q_(k) and R_(k). It is possiblethat an interpolation technique may be employed in this stage, ratherthan explicitly computing each QR decomposition on a per-sub-carrierbasis.

Steps S-12 and S-14 are repeated for each subcarrier in a set, asindicated with regard to step S2-16.

The method therefore yields the outputs Q_(k) and R_(k) on aper-sub-carrier basis and T which is common to the set of sub-carriers.These outputs can be employed in the subsequent stages of a latticereduction aided detector (or pre-coder) in the same way as the outputsof a per-sub-carrier lattice reduction method. This method is thereforesub-optimal, in that a common T is employed for the set whereas in theper-sub-carrier processing algorithm an optimal T_(k) is obtainedper-sub-carrier.

The complexity reduction of this method stems from the fact that thereis only a single LLL function and K+1 QR decompositions per K groupedsub-carriers, whereas in the per-sub-carrier case, K LLL functions and KQR decompositions are required. For this to yield a significantcomplexity reduction, the QR decomposition must have significantly lowercomplexity than the LLL reduction, as the number of QR decompositionsrequired is increased by 1 per set. The complexity of the LLL reductionis variable, but in general, the LLL reduction will have greatercomplexity than the QR decomposition.

A further embodiment of the invention will now be described withreference to FIG. 5, in which steps S3-2 to S3-12 correspond directly tosteps S2-2 to S2-12 as previously described. The described method offersadditional complexity saving, using additional lattice reduction stagesS3-16 (employing a permutation matrix T determined in step S3-20) afterthe per-sub-carrier QR decompositions S3-14 in the grouped method. Thepurpose of these additional lattice reduction stages is to refine thecommon T, produced by the grouped technique, into per-sub-carrier (orsmaller set) basis reductions. An individual basis reduction can beobtained by using the reduction:[T_(k),{tilde over (Q)}_(k),{tilde over (R)}_(k)]=LLL({tilde over(Q)}_(k),{tilde over (R)}_(k), T)It is important to note that the permutation matrix input to the LLLreduction is in this case not initialised to the identity matrix, but isinitialised to T.

This refinement adds additional complexity to the per-sub-carriermethod, but will result in a more accurate lattice reduction. Assumingthat the common T is a good approximation to T_(k), then the additionalcomplexity involved in the refinement LLL should be minimal.

FIG. 6 shows the performance of the basic sub-carrier grouping techniquein comparison with the per-sub-carrier method. Results are for an802.11n MIMO-OFDM system, over a channel with limited delay-spread (andtherefore frequency-selectivity). This channel is a good model forcommon indoor operating environments and is therefore representative ofa real world scenario. Set sizes of 4 and 8 sub-carrier groupings areshown for two modulation and coding scheme (MCS) values. These resultsdemonstrate that, for this operating environment, only minimaldegradation in performance is observed with grouping sizes that willresult in significant complexity reduction. For example, for MCS valueof 11, the degradation at a 1% Packet Error Rate (PER) associated withthe use of a set size of 8 is only 1 dB compared to per-sub-carrierprocessing.

The person skilled in the art will appreciate that the description abovecan also be applied to a MIMO pre-coder.

It will be appreciated that the foregoing provides description ofspecific embodiments of the invention and that no limitation on thescope of protection sought herein is to be implied therefrom. The scopeof protection sought is to be determined from the claims, read withreference to, but not bound by, the description and drawings.

1. A method for determining outputs from a received signal in alattice-reduction-aided receiver based multi-carrier wirelesscommunications system having a plurality of sub-carriers divided into aplurality of sets of sub-carriers, the method comprising performing adetection method for each of said sets, the detection method comprisingthe step of applying lattice reduction to said set of sub-carriersthereby generating a reduced basis channel response.
 2. A method inaccordance with claim 1 further comprising the step of determining asingle value channel response matrix from a set of channel responsematrices.
 3. A method in accordance with claim 2, wherein the step ofdetermining said single value channel response is performed by any oneof: i. mean value of said channel response matrices, and; ii. medianvalue of said channel response matrices.
 4. A method in accordance withclaim 1 further comprising the step of processing said single valuechannel response matrix thereby generating an unitary matrix and atriangular matrix.
 5. A method in accordance with claim 4, wherein thestep of processing said single value channel response matrix is a QRdecomposition of said single value channel response matrix.
 6. A methodin accordance with claim 4, wherein the step of applying said latticereduction to said plurality of sub-carriers includes the step ofapplying said lattice reduction to said unitary matrix and saidtriangular matrix.
 7. A method in accordance with claim 1 furthercomprising the step of determining a reduced basis of a sub-carrier inaccordance with said reduced basis channel response.
 8. A method inaccordance with claim 7 further comprising the step of determining anunitary matrix and a triangular matrix for said sub-carrier.
 9. A methodin accordance with claim 8, wherein the step of determining said unitarymatrix and said triangular matrix for said sub-carrier is performed byany one of: i. A QR decomposition, and; ii. An interpolation method. 10.A method in accordance with claim 1, wherein the lattice reduction is inaccordance with the LLL algorithm.
 11. A method in accordance with claim7, further comprising the step of applying lattice reduction to saidunitary matrix and said triangular matrix to said sub-carrier has thefollowing relationship:[T_(k),{tilde over (Q)}_(k),{tilde over (R)}_(k)]=LLL({tilde over(Q)}_(k),{tilde over (R)}_(k), T) where T is a permutation matrix. 12.An apparatus for determining outputs from a received signal in alattice-reduction-aided receiver based multi-carrier wirelesscommunications system having a plurality of sub-carriers divided into aplurality of sets of sub-carriers, the apparatus comprising detectionmeans for performing detection on each of said sets, the detection meanscomprising means for applying lattice reduction to said sub-carriers insaid set thereby generating a reduced basis channel response.
 13. Anapparatus in accordance with claim 12 further comprising means fordetermining a single value channel response matrix from a set of channelresponse matrices.
 14. An apparatus in accordance with claim 13, whereinsaid means for determining said single value channel response isoperable to determine any one of: i. mean value of said channel responsematrices, and; ii. median value of said channel response matrices. 15.An apparatus in accordance with claim 12 further comprising means forprocessing said single value channel response matrix to generate aunitary matrix and a triangular matrix.
 16. An apparatus in accordancewith claim 15, wherein said processing means is operable to perform a QRdecomposition of said single value channel response matrix.
 17. AMIMO-OFDM wireless communications apparatus including a detectorcomprising apparatus in accordance with claim
 12. 18. A computer programproduct comprising computer executable instructions which, when executedon a computer controlled communications apparatus, cause the apparatusto become configured to perform the method of claim
 1. 19. A storagemedium storing computer executable instructions which, when executed ona computer controlled communications apparatus, cause the apparatus tobecome configured to perform the method of claim
 1. 20. A signalcarrying computer receivable information, the information definingcomputer executable instructions which, when executed on a computercontrolled communications apparatus, cause the apparatus to becomeconfigured to perform the method of claim 1.